Math 403H   Honors Classical Analysis I   Fall 2021

   Class meets:   Monday, Wednesday, Friday  2:30-3:20 p.m.  in 268 Willard

   Office hours:  

Victoria Sadovskaya            
426 McAllister
(814) 863-4140
Monday & Friday 1:20-2:10 p.m.,  Wednesday 3:40-4:30 p.m.,
and by appointment

    Text:  Real Analysis  by N.L. Carothers.

    Course description: The goal of this course is to develop thorough understanding and
    technical mastery of foundations of classical analysis in the framework of metric spaces.
    The following topics will be covered:  Metric spaces (open and closed sets, connectedness,
    convergence, Cauchy sequences and completeness);  Maps between metric spaces (continuous
    maps and homeomorphisms, stronger continuity properties, contraction mapping principle);
    Compact metric spaces (continuity and compactness, total boundedness, coverings);
    Baire Category Theorem;  Function spaces (spaces of continuous maps, equicontinuity,
    Arzela-Ascoli Theorem, Stone-Weierstrass Theorem).
    Prerequisites: Math 311M and Math 312H.

    Syllabus    pdf



    Exam 1 will take place on Wednesday, October 6. It will cover Chapters 2-5.   Study guide   
    Exam 2 will take place on Wednesday, November 10.


    Fall 2021 Academic Calendar